%0 Journal Article
%T From Coalgebra to Bialgebra for the Six-Vertex Model: The Star-Triangle Relation as a Necessary Condition for Commuting Transfer Matrices
%A Jeffrey R. Schmidt
%J Axioms
%D 2012
%I MDPI AG
%R 10.3390/axioms1020186
%X Using the most elementary methods and considerations, the solution of the star-triangle condition (a2+b2-c2)/2ab = ((a¡¯) ^2+(b¡¯) ^2-(c¡¯)) ^2/2a¡¯b¡¯ is shown to be a necessary condition for the extension of the operator coalgebra of the six-vertex model to a bialgebra. A portion of the bialgebra acts as a spectrum-generating algebra for the algebraic Bethe ansatz, with which higher-dimensional representations of the bialgebra can be constructed. The star-triangle relation is proved to be necessary for the commutativity of the transfer matrices T(a, b, c) and T(a¡¯, b¡¯, c¡¯).
%K vertex model
%K bialgebra
%K coalgebra
%K Bethe ansatz
%U http://www.mdpi.com/2075-1680/1/2/186